The regulator for Fannie Mae and Freddie Mac could have a “legal responsibility” to approve loan modifications for certain homeowners now that the U.S. Treasury has offered to share in the cost of mortgage write-downs, said Shaun Donovan, secretary of the U.S. Department of Housing and Urban Development.

Mr. Donovan made the comments in an interview taped Friday for C-SPAN’s “Newsmakers” program. He said that he was increasingly worried that given the severity of the collapse in home prices and the slow pace of recovery in certain housing markets, that some homeowners who owe far more than their homes are worth would conclude “there is really no light at the end of the tunnel” and ultimately default on their mortgage.

In certain hard-hit markets, families struggling to make payments “will give up at some point. We think the data shows that.” The administration’s analysis of various housing markets makes a “compelling” case for principal write-downs, he added.

But at the same time, Mr. Donovan downplayed concerns that borrowers who are deeply underwater but able to pay their loans would similarly default in order to receive debt reduction. “The vast majority of homeowners don’t operate that way,” he said.

Edward DeMarco, the acting director of the Federal Housing Finance Agency, has so far resisted principal forgiveness, arguing that other means of reducing payments are just as successful with fewer costs for taxpayers that are backing the mortgage giants.

One concern for that regulator is whether debt forgiveness would encourage more borrowers who are current on their loans to stop paying. Right now, about three in four loans backed by Fannie and Freddie that are heavily underwater are still making regular payments. “These borrowers are demonstrating a continued willingness to meet their mortgage obligations. This should be recognized and encouraged, not dampened with incentives for people to not continue paying,” said Mr. DeMarco in a speech this past week.

Mr. Donovan said for those cases where borrowers might strategically default, there are ways to carefully design a program “to ensure that it doesn’t become a real issue.”

The Obama administration in January offered to subsidize the write-downs, undercutting the position of Mr. DeMarco, who has promised to give an answer to the administration later this month.

Mr. Donovan said that his experience with Mr. DeMarco suggested that the regulator would make an impartial decision. “What he is focused on, independent of whatever his personal views may be, is what is his legal responsibility and what does the analysis say.”

Mr. Donovan also said he wouldn’t “prejudge” what the administration would do if Mr. DeMarco chose not to allow the firms to participate. If that happens, “we’re going to have to look at that analysis and understand what his concerns are,” he said.

Several Democratic lawmakers and political groups have called on the Obama administration to fire Mr. DeMarco over his resistance to debt forgiveness, but Republicans say that write-downs amount to transfers of taxpayer wealth. Economists on both sides of the issue have offered research highlighting the benefits and drawbacks of debt forgiveness.

In the interview, Mr. Donovan said that the ultimate success of the Obama administration’s housing policies would be determined by the future path of home prices and “whether the average American once again has faith that buying a home is something that is a safe investment in the long term.”

The housing secretary pointed to recent signs of improved home sales during the winter months, but home prices have been falling during the winter months. “Ultimately, the final measure of whether we’ve broken through and we’re in full recovery is when housing prices across the board start rising in a consistent way,” he said.